I search the IFHF database at rootsireland.ie. It contains 19 million B/M/D records for most, but not all of Ireland.
For George Moffat B 1824 +/- 1 yr, somewhere in Ireland, with the parents names unknown, I found 1 record in 1823, Co. Donegal. The father's forename associated with this record is James. The mother's forname is Jane.
These findings may be false positives, but merit a view of the detailed record with a small IFHF fee.
Suggest you at least register (free) with the IFHF. It will notify you as additional records are added. Note - 1824 is VERY early for Irish records. There is a 50% chance that the record did not survive.